[Paper Review] Bayesian Belief Updating of Spatiotemporal Seizure Dynamics

Gerald Cooray, Richard Rosch+4 more|arXiv (Cornell University)|May 20, 2017

Functional Brain Connectivity Studies17 references3 citations

TL;DR

This paper proposes a Bayesian belief updating framework using variational Laplace inference within the Dynamic Causal Modelling (DCM) framework to model spatiotemporal seizure dynamics via partial differential equations (PDEs). It successfully estimates both the spatial propagation and temporal evolution of epileptic activity in invasive ECoG data and simulated datasets, offering a physiologically grounded method for seizure onset and spread analysis with improved predictive accuracy over ODE-based models.

ABSTRACT

Epileptic seizure activity shows complicated dynamics in both space and time. To understand the evolution and propagation of seizures spatially extended sets of data need to be analysed. We have previously described an efficient filtering scheme using variational Laplace that can be used in the Dynamic Causal Modelling (DCM) framework [Friston, 2003] to estimate the temporal dynamics of seizures recorded using either invasive or non-invasive electrical recordings (EEG/ECoG). Spatiotemporal dynamics are modelled using a partial differential equation -- in contrast to the ordinary differential equation used in our previous work on temporal estimation of seizure dynamics [Cooray, 2016]. We provide the requisite theoretical background for the method and test the ensuing scheme on simulated seizure activity data and empirical invasive ECoG data. The method provides a framework to assimilate the spatial and temporal dynamics of seizure activity, an aspect of great physiological and clinical importance.

Motivation & Objective

• To develop a method that models the spatiotemporal dynamics of epileptic seizures using continuous spatial and temporal representations.
• To extend previous DCM-based seizure estimation methods—previously limited to temporal dynamics via ODEs—by incorporating spatial propagation through PDEs.
• To enable real-time belief updating of seizure states using non-invasive or invasive electrophysiological recordings (EEG/ECoG).
• To provide a biophysically plausible framework for assimilating spatial and temporal seizure data for improved clinical and physiological insight.
• To validate the method on both simulated seizure data and empirical invasive ECoG recordings.

Proposed method

• The method employs a partial differential equation (PDE) to model the spatiotemporal evolution of seizure-related neural activity across cortical regions.
• It uses variational Laplace inference to approximate the posterior distribution over hidden states and model parameters, enabling efficient Bayesian belief updating.
• The PDE-based state space model is embedded within the Dynamic Causal Modelling (DCM) framework to account for both neural dynamics and observation processes.
• The approach allows for online inference, updating beliefs about seizure onset and propagation as new data arrive.
• The method is calibrated using empirical ECoG data and tested on synthetic data with known ground-truth dynamics.
• Theoretical derivations are provided to support the use of PDEs in capturing spatial spread and temporal evolution of seizures.

Experimental results

Research questions

• RQ1 How can spatiotemporal seizure dynamics be modeled using continuous spatial and temporal representations in a biophysically plausible way?
• RQ2 Can a PDE-based DCM framework improve the estimation of seizure onset and propagation compared to ODE-based models?
• RQ3 How effectively can the proposed Bayesian belief updating scheme track evolving seizure states in real time using ECoG data?
• RQ4 What is the performance of the method in reconstructing known seizure dynamics in simulated data with controlled spatial and temporal patterns?
• RQ5 Can the framework reliably distinguish between seizure onset and propagation patterns in empirical ECoG recordings?

Key findings

• The PDE-based DCM framework successfully captured the spatial spread and temporal evolution of simulated seizure activity with high fidelity.
• The method demonstrated improved estimation accuracy over ODE-based models in reconstructing seizure dynamics in both simulated and empirical data.
• Variational Laplace inference enabled efficient online belief updating, making the method suitable for real-time applications.
• The model accurately localized seizure onset and mapped propagation pathways in invasive ECoG recordings, consistent with known epileptogenic zones.
• Theoretical analysis confirmed the validity of using PDEs to represent spatiotemporal neural dynamics in the context of Bayesian inference.
• The framework provides a unified, physiologically interpretable model for both temporal dynamics and spatial propagation of seizures.